We consider the problem of choosing an alternative in a set A = {A1, A2, ..., Am} of alternatives, given a set D = {d1, d2, ..., dh} of decision makers and a set Ω = {O1, O2, ..., On} of objectives. We assume that any decision maker dk assigns to any pair (alternative Ai, objective Oj) a number aijk that measures to what extent Ai satisfies Oj . We assume that Ω is a subset of a universal set U...

We define and study the concept of non-Archimedean intuitionistic fuzzy normed space by using the idea of t-norm and t-conorm. Furthermore, by using the non-Archimedean intuitionistic fuzzy normed space, we investigate the stability of various functional equations. That is, we determine some stability results concerning the Cauchy, Jensen and its Pexiderized functional equations in the framewor...

We present a procedure for the construction of multi-valued t-norms and t-conorms. Our procedure makes use of a pair of single-valued t-norms and the respective dual t-conorms and produces interval-valued t-norms u and t-conorms t. In this manner we combine desirable characteristics of different t-norms and t-conorms; if we use the t-norm ∧ and t-conorm ∨, then (X,u,t) is a superlattice, i.e. t...

We study the weak duality S(x, N (x)) = N (T (x, N (x))) where S is a continuous t-conorm, T is a continuous t-norm and N is a strong negation. We characterize completely the strict cases and show that in all other cases there is no direct relation between generators of T and S or between their possible Archimedean components in ordinal sums.

In this article, we introduce the idea of normality and translation Q-intuitionistic fuzzy subgroups with respect to norms (t-norm T t-conorm C) some interesting results them are given. Conditions for level cut subsets explored provided. Finally, investigate by using group homomorphisms investigated.

We present a procedure for constructing multi-valued tnorms and t-conorms. Our construction uses a pair of single-valued t-norms and the pair of dual t-conorms to construct interval-valued t-norms u and t-conorms t. In this manner we can combine desirable characteristics of different t-norms and t-conorms; furthermore if we use the t-norm ∧ and t-conorm ∨, then (X,u,t) is a superlattice, i.e. t...

We consider the generalized method-of-case (GMC) inference scheme with fuzzy antecedents, which has been introduced by Da in [1]. We show that when the fuzzy numbers involved in the observation part of the scheme have continuous membership functions; and the t-norm, t-conorm used in the definition of the membership function of the conclusion are continuous, then the conclusion defined by the co...

Fuzzy integrals are commonly used as aggregation operators. In this paper we present new composite models based on fuzzy integrals with several t-conorms. These models permit to further increase the computational power of the previous models. Basic properties of new composite models are studied. In particular, it is shown that for composite models, the only meaningful case is when not all the t...

The Dombi operations of T-norm and T-conorm introduced by Dombi can have the advantage of good flexibility with the operational parameter. In existing studies, however, the Dombi operations have so far not yet been used for neutrosophic sets. To propose new aggregation operators for neutrosophic sets by the extension of the Dombi operations, this paper firstly presents the Dombi operations of s...

Archimedean t-conorm and t-norm are generalizations of a lot of other t-conorms and t-norms, such as Algebraic, Einstein, Hamacher and Frank t-conorms and t-norms or others, and some of them have been applied to intuitionistic fuzzy set, which contains three functions: the membership function, the nonmembership function and the hesitancy function describing uncertainty and fuzziness more object...